Answer
$$A = \frac{{26}}{{\ln 3}}$$
Work Step by Step
$$\eqalign{
& y = {3^x},{\text{ }}y = 0,{\text{ }}x = 0,{\text{ }}x = 3 \cr
& {\text{From the graph, we can define the area enclosed by}} \cr
& A = \int_0^3 {{3^x}} dx \cr
& {\text{Integrating}} \cr
& A = \frac{1}{{\ln 3}}\left[ {{3^x}} \right]_0^3 \cr
& A = \frac{1}{{\ln 3}}\left[ {{3^3} - {3^0}} \right] \cr
& A = \frac{{27 - 1}}{{\ln 3}} \cr
& A = \frac{{26}}{{\ln 3}} \approx 23.66 \cr} $$